Why is only part of my render taking so long? Did I do something wrong? (Cycles)
Rendering takes time.

Rendering complex scene takes more time than simple scenes.

The higher the number of particles the longer it will take to render.

Using a large number of subdivisions in the subsurf modifier will increase the number of polygon on the scene, further increasing the computation needed to render the scene.

Simulations will also use more resources and stress your computer. 

Not all segments of an animation will take the same time to render,  it all depends on the elements used for each frame in the scene. 

It seems to me that your scene exceeds the resources of your hardware. You don't state how much ram your system has, but chances are your system is running on virtual memory and going slower.

There are many things you can do to optimize your scene: Bake all simulations, reduce the complexity of your geometry, render in different layers and composite later, reduce the size of the image textures used. Maybe bake some of the materials...

As a side note: Never render complex animations as mpeg directly. Render as an image sequence and encode as video later, you'll be very disappointed if after such long renders your computer crashes and you realize all of the previously rendered frames are gone, and you have to start over.Rendering as image sequences will also allow you to stop the rendering process to use your computer and resume later.

I doubt there is anything wrong with the file itself.... You didn't pack your textures with the file, so it's hard to asses the scene properly. (Frame 166 rendered in 39 seconds using GPU on my system...)